CSCAPrep
Reviewed CSCA Mathematics question · Hard

A circle has its center at (3, -1) and passes through the point (7, 2). What is the circumference of the circle?

  1. 5π
  2. 10π
  3. 25π
  4. 20π
Show the answer and explanation

Correct answer

B. 10π

Principle or equation

The radius is the distance from the center to a point on the circle. Circumference = 2πr.

Why this answer is correct

Distance from (3,-1) to (7,2) is sqrt((7-3)^2 + (2-(-1))^2) = sqrt(16+9) = sqrt(25) = 5. So radius r = 5. Circumference = 2π*5 = 10π.

Example

For a circle centered at (0,0) passing through (3,4), radius = 5, circumference = 10π.

This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.

Related practice questions

Easy · Geometry and algebraWhat is the product (2 + 3i)(1 - i)?Standard · Geometry and algebraWhat is the center of the circle given by x^2 + y^2 - 4x + 6y - 3 = 0?Easy · Geometry and algebraGiven vectors u = (3, -2) and v = (1, 4), what is 2u - v?Easy · Geometry and algebraA rectangular box has vertices at (0,0,0), (4,0,0), (0,3,0), and (0,0,12). What is the length of the space diagonal of this box?Standard · Geometry and algebraWhat is the value of (3 + 2i) / (1 - i)?